Hankel operators with antiholomorphic symbols on the Fock space

Schneider, Georg

doi:10.1090/S0002-9939-04-07362-9

Hankel operators with antiholomorphic symbols on the Fock space
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Proc. Amer. Math. Soc. 132 (2004), 2399-2409 Request permission

Abstract:

We consider Hankel operators of the form $H_{\overline {z}^k}: \mathcal {F}^m:=\{f : f \mbox { is entire and} \int _{\mathbb {C}^n}|f(z)|^2e^{-|z|^m}<\infty \}\rightarrow L^2(e^{-|z|^m})$. Here $k,m,n \in \mathbb {N}$. We show that in the case of one complex dimension the Hankel operators are compact but not Hilbert-Schmidt if $m>2k$.

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